Consider significant figures in your calculations.

How many significant figures are there in the following numbers?

- 0.000350
- 0.0350
- 3.50
- 350.

All of them have three significant figures.

How many digits do you need to keep?

Suppose you are given a number of data and you want to use these data to calculate a result from a formula. Often the number of significant figures in the final result is rounded such that it is the same as the least number of significant figures in the given data. Sometimes an extra digit is kept.

Example:
A particle has a displacement of Dx
= 10.000 m during time interval Dt
= 3.0 s. Find the average velocity v_{avg}
during this time interval.

v_{avg} = Dx /Dt
= 10.000/3.0 m/sec.

If you try to calculate the final answer with a calculator, you will get 3.333333333. Since the least number of significant figures in our data is that of Dt, which has two significant figures, the accuracy implied by the result from our calculator is meaningless. We need to round our result to two significant figures.

v_{avg} = 3.3 m/s

It is also acceptable to use thee significant figures in our
result that is v_{avg} = 3.33 m/s but not more.

How do you round a number?

When the leftmost of the digits to be discarded is 5 or more, the last remaining digit is rounded up; otherwise it is retained as is.

Example: Round the following numbers to three significant figures

10.25678→ 10.3

0.3252567

→
0.325